Converting units for area and volume

The method for converting between units works the same as the one for converting units of area and volume.

When you are converting one sort of unit to another, you need to know how many smaller units are needed to make {1} larger unit.

For example: 1~km^{2} = 1~km \times 1~km

1,000~m \times 1,000~m

1,000,000~m^{2}

  • When converting from a larger unit to a smaller unit (eg m^2 to cm^2), you multiply.
  • When converting from a smaller unit to a larger unit (eg mm^2 to cm^2), you divide.

Example 1

Convert 50,000~cm^2 into m^2.

1~m = 100~cm.

Diagram of squares

So, 1~m^2 = 100~cm \times 100~cm = 10,000~cm^2.

You are converting from a smaller unit (cm^2) to a larger unit (m^2), so divide.

50,000~cm^2 = 50,000 \div 10,000 = 5~m^2.

Example 2

Convert 10~cm^3 into mm^3.

1~cm = 10~mm.

Diagram of cubes

So, {1}~cm^{3} = {10}~mm\times{10}~mm\times{10}~mm = {1,000}~mm^{3}.

You are converting from a larger unit (cm^3) to a smaller unit (mm^3), so multiply.

{10}~cm^{3} = {10}\times{1,000} = {10,000}~mm^{3}